承压井水位观测系统对体应变的响应机制分析
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摘要
本文基于弹性力学与流体静力学原理对承压含水层这种弹性孔隙介质在作用力激励下所作出的体应变响应的力学机制进行了较清晰深入的阐述与理论推导,得到了井水位系统的动力学方程,该方程表明井水位系统为一个零阶的放大环节,其传递函数为一常数,从而给出了在含水层孔隙度分别等于零和等于1情况下的井水位系统所允许的理论格值范围.鉴于井水位系统为一个天然体应变计,其维尼迪柯夫调和分析所得到的振幅比(或潮汐因子)即为该水井的传递函数(灵敏度).由于半日波为水位观测资料的主项,而M2波又为半日波的主项,因此以M2波灵敏度的倒数作为该井水位系统的格值是较为可取的.在取得格值的基础上,本文利用福建5口水井2008年5月份的井水位分钟值对发生在5月12日的四川汶川地震所引起的同震阶变进行计算,四川汶川大地震所引起的这5口水井的水震波幅度与体应变潮汐波幅度约为10~(-7)～10~(-8).
Based on principles of viscoelastic mechanics and hydrostatics,this paper expounds the dynamic mechanism of cubic strain response to excitation force in the confined aquifer and derives its theoretical formula.The result shows that the dynamics equation of well water-level system is an amplifying link of zero-order.It also shows that its transfer function is a constant.According to these results,the allowable bounds of theoretical calibration value η of water-level system were determined when the porosity of the confined aquifer is zero or one.Whereas the well-water-level system is a natural cubic strain gauge,the amplitude ratio (tide factor) computed by Venidikov s harmonic analysis method is the transfer function (sensitivity) of the system.Because wave M2 is the main component of the semidiurnal wave which is the main component of the observation data of ground water level,the paper takes the reciprocal of the amplitude ratio (sensitivity) of wave M2 as the theoretical value η of well water-level system.With this theoretical calibration value η, the water-level seismic wave excited by Wenchuan earthquake is calculated through the minute values of observation of well water level of five wells in May,2008.The calculated result shows that the amplitude of seismic water-level wave is the same as the cubic strain wave of the planet Earth at approximately the order of magnitude 10~(-7)～10~(-8).
Based on principles of viscoelastic mechanics and hydrostatics,this paper expounds the dynamic mechanism of cubic strain response to excitation force in the confined aquifer and derives its theoretical formula.The result shows that the dynamics equation of well water-level system is an amplifying link of zero-order.It also shows that its transfer function is a constant.According to these results,the allowable bounds of theoretical calibration value η of water-level system were determined when the porosity of the confined aquifer is zero or one.Whereas the well-water-level system is a natural cubic strain gauge,the amplitude ratio (tide factor) computed by Venidikov s harmonic analysis method is the transfer function (sensitivity) of the system.Because wave M2 is the main component of the semidiurnal wave which is the main component of the observation data of ground water level,the paper takes the reciprocal of the amplitude ratio (sensitivity) of wave M2 as the theoretical value η of well water-level system.With this theoretical calibration value η, the water-level seismic wave excited by Wenchuan earthquake is calculated through the minute values of observation of well water level of five wells in May,2008.The calculated result shows that the amplitude of seismic water-level wave is the same as the cubic strain wave of the planet Earth at approximately the order of magnitude 10~(-7)～10~(-8).
引文
[1] P·梅尔基奥尔著.行星地球的固体潮.杜品仁,吴庆鹏,陈益惠等译.北京:科学出版社,1984． 145-247 Melchior P.The Tides of the Planet Earth.Translated by Du PinRen,Wu QingPeng,Chen YiHui,et al.Beijing:Science Press,1984． 145-247
[2] 王吉易,董守玉,陈建民.地下流体地震预报方法.北京:地震出版社,1997． 14-65 Wang J Y,Dong S Y,Chen I M.The Methods of Earthquake Prediction Through Subsurface Fluid Observation (in Chinese).Beijing:Seismological Press,1997,14-65
[3] Paul P U.College Physics.Beijing:Mechanical Industry Press,2003． 135-253
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[6] 毛根海,邵卫云,张燕.应用流体力学.北京:高等教育出版社,2006． 17-24 Mao G H,Shao W Y,Zhang Y.Application of Fluid MechanicsCin Chinese).Beijing:Higher Education Press,2006． 17-24
[7] W·杨,R·布迪纳斯.应力应变公式手册.岳珠峰,高行山,王峰会等译.北京:科学出版社,2005． 11-14 Young W C,Budynas R G.Handbook of Stress and Strain Formulas.Translated by Yue Z F,Gao X S,Wang F H,et al.Beijing:Science Press,2005． 11-14
[8] 郭伟国,李玉龙,索涛.应力波基础简明教程.西安:西北大学出版社,2007． 12-17 Guo W G,Li Y L,Suo T.A Concise Course of the Stress Wave C in Chinese).Xi an:Northwest University Press,2007． 12-17
[9] 傅承义,陈运泰,祁贵仲.地球物理学基础.北京:科学出版社,1985． 276-334 Fu C Y,Chen Y T,Qi G Z.Foundations of Earth Physics(in Chinese).Beijing:Science Press,1985． 276-334
[10] Jaeger J C.Elasticity,Fracture and Flow,212 pp.,Methuen & Co.,London,1964,54-58
[11] Shearer P M.Introduction to Seismology.Cambridge Press, 1999． 15
[12] 王敏中.王炜,武际可.弹性力学教程.北京:北京大学出版社,2002． 80-84 Wang M Z,Wang W,Wu J K.The Course of Elastic Mechanics(in Chinese).Beijing:Beijing University Press,2002． 80-84
[13] A阿拉比,M阿拉比.简明牛津地球科学辞典.陈有发,汤泉,张杰等译.北京:地震出版社,1998． 461 Allaby A,Allaby M.The Concise Oxford Dictionary of Earth Science.Translated by Chen YouFa,Tang Quan,Zhang Jie,et al.Beijing:Seismological Press,1998． 461
[14] Horst Stocker编.物理手册.吴锡英,李祝霞,陈师平译.北京:北京大学出版社,142 Horst Stocker.Physical Handbook.Translated by Wu Xiying,Li Zhuxia,Chen Shi-ping.Beijing:Beijing University Press,142
[15] 万迪堃,汪成民.地下水动态异常与地震短临预报.北京:地震出版社,1993． 10-146 Wan D K,Wang C M.Ground Water Dynamic Anomaly and Short-Term Earthquake Prediction ( in Chinese).Beijing:Seismological Press,1993． 10-146
[16] 敬少群,王佳卫.长沙井动水位对台湾集集7． 6级地震的震时效应及其机理分析.华南地震,2001,21(1) :32-37 Jing S Q,Wang J W.Analysis on seismic effect and its mechanism of Changsha well's dynamic ground water level for the M_s7． 6 Jiji earthquake,Taiwan.South China Journal of Seismology (in Chinese),2001,21(1) :32-37
[17] 张素欣,杨卫东,张子广.唐山矿井模拟与数字水位的记震能力对比分析.西北地震学报,2007,29(2) :170-173 Zhang S X,Yang W D,Zhang Z G.Comparison of the ability of recording seismic wave between digital and analogue groundwater level observation in Tangshan mine well.Northwestern Seismological Journal (in Chinese),2007,29 (2) :170-173
[18] 郑小菁,陈莹.福建数字地下流体网对远处大震映震能力分析.国际地震动态,2007,3:31-37 Zheng X J,Chen Y.Analysis on the reflecting capacity for large distant earthquakes by use of digital underground water monitoring network in Fujian Province.Recent Developments in World Seismology (in Chinese),2007,3:31-37
[19] 晏锐,陈颙,高福旺等.从昌平井体应变、水位对地震波的响应特征求算含水层的SKEMPTON常数.地震学报,2008,30(2) :144-152 Yan R,Chen Y,Gao F W,et al.Calculating B value of aquifer from volume strain and water level response to seismic waves at Changping seismic station.Acta Seismologica Sinica (in Chinese),2008,30(2) :144-152
[20] 《地球科学大辞典》编委会编.地球科学大辞典(基础科学卷).北京:地质出版社,2006． 1-4 The Editorial Committee eds.《Geoscience Big Dictionary》(Basic science volume) (in Chinese).Beijing:Geological Publishing House,2006． 1-4
[21] 汪成民,车用太,万迪堃等.地下水微动态研究.北京:地震出版社,1988． 20-23 Wang C M,Che Y T,Wan D K,et al.Ground Water Micro Dynamics Research (in Chinese).Beijing:Seismological Press,1988,20-23
[22] 国家地震局科技监测司.地震地下流体观测技术.北京:地震出版社,1995． 19 Science,Technology and Monitoring Department of China Earthquake Administration.Seism-Related Underground Fluid Observation Technology ( in Chinese ).Beijing:Seismological Press,1995． 19
[23] 曾劲主编.控制工程基础.北京:电子工业出版社,2007． 18 Edited by Zeng Jing.Control Engineering Foundation (in Chinese).Beijing:Publishing House of Electronics Industry,2007． 18
[24] 陆一心主编.现代工程控制理论.北京:化学工业出版社,2006． 12-21 Edited by Lu YiXin.Modern Engineering Control Theory(in Chinese).Beijing:Chemical Industry Publishing House, 2006． 12-21
[25] 北京大学地球物理系,武汉测绘学院大地测量系,中国科学技术大学地球物理教研室编.重力与固体潮.北京:地震出版社,1982． 349-360 The Earth Physics Department of Peking University,the Geodetic Survey Department of Wuhan Survey Institute,the Geophysics Staff Room of University of Science and Technology of China.Gravity and Earth Tide (in Chinese).Beijing:Seismological Press,1982． 349-360
[26] 张昭栋等.地下水潮汐分析.济南:山东大学出版社,1988． 15-18 Zhang Z D et al.Ground Water Tide Analysis (in Chinese).Jinan:Shandong University Press,1988． 15-18
[27] Brodsky E E,Roeloffs E,Woodcook D,et al.A mechanism for sustained groundwater pressure changes induced by distant earthquakes.Journal of Geophysical Research,2003,108(B8) ,2390,doi:1029/ 2002JB002321,2003,SDE10． 1-10． 4
[28] 邱永平.宁波地震台水位、地倾斜在印尼8． 7、 8． 5级地震中的同震变化现象.内陆地震,2006,20(4) :336-341 Qiu Y P.The phenomenon of co-seism change about water level and the tile of Ningbo seismic station in Indonesia earthquakes with M_s 8． 7 and M_s8． 5． Inland Earthquake (in Chinese),2006,20(4) :336-341
[29] Chia Y P,Wang Y S,Chiu J J,et al.Changes of ground water level due to the 1999 Chi-Chi earthquake in the Choshui River Alluvial Fan.Bulletin of Seismological Society of America,2001,91(5) :1062-1068
[30] Thorne L,Terry C W.Modern Global Seismology.Academic Press,1981． 34-125
[31] 郑小菁,刘序俨,韦永祥,陈莹.采用主成分分析方法研究降水对地下水位的影响.地震,2008,28(4) :91-102 Zheng X J,Liu X Y,Wei Y X,Chen Y.Analysis of effect of precipitation to underground water level of Qingyang stressed well of Fujian Province.Earthquake (in Chinese),2008,28 (4) :91-102
[32] Simon B.Oxford Dictionary of Philosophy.Shanghai:Shanghai Foreign Language Education Press,2000． 267-268
[33] 尹宝军,马丽,陈会忠等.汶川8． 0级地震及其强余震引起的唐山井水位同震响应特征分析.地震学报,2009,31(2) :195-205 Yin B J,Ma L,Chen H Z,et al.Characteristics of coseismic water level change in Tangshan well induced by M_s8． 0 Wenchuan earthquake and its large aftershocks.Acta Seismologica Sinica (in Chinese),2009,31(2) :195-205
[2] 王吉易,董守玉,陈建民.地下流体地震预报方法.北京:地震出版社,1997． 14-65 Wang J Y,Dong S Y,Chen I M.The Methods of Earthquake Prediction Through Subsurface Fluid Observation (in Chinese).Beijing:Seismological Press,1997,14-65
[3] Paul P U.College Physics.Beijing:Mechanical Industry Press,2003． 135-253
[4] Burce R M,Donald F Y,Theodore H O.Fundamentals of Fluid Mechanics.Beijing:Publishing House of Electronics Industry,2006． 2-19
[5] E·约翰芬纳莫尔,约瑟夫B·弗朗兹尼.流体力学及其工程应用.钱翼稷,周玉文等译.北京:机械工业出版社,2006． 9-16 Finnemore E J,Franzini JB.Hydrodynamics and Its Engineering Applications (in Chinese).Translated by Qian YiJi-Zhou YuWen et al.Beijing:Mechanical Industry Press,2006． 9-16
[6] 毛根海,邵卫云,张燕.应用流体力学.北京:高等教育出版社,2006． 17-24 Mao G H,Shao W Y,Zhang Y.Application of Fluid MechanicsCin Chinese).Beijing:Higher Education Press,2006． 17-24
[7] W·杨,R·布迪纳斯.应力应变公式手册.岳珠峰,高行山,王峰会等译.北京:科学出版社,2005． 11-14 Young W C,Budynas R G.Handbook of Stress and Strain Formulas.Translated by Yue Z F,Gao X S,Wang F H,et al.Beijing:Science Press,2005． 11-14
[8] 郭伟国,李玉龙,索涛.应力波基础简明教程.西安:西北大学出版社,2007． 12-17 Guo W G,Li Y L,Suo T.A Concise Course of the Stress Wave C in Chinese).Xi an:Northwest University Press,2007． 12-17
[9] 傅承义,陈运泰,祁贵仲.地球物理学基础.北京:科学出版社,1985． 276-334 Fu C Y,Chen Y T,Qi G Z.Foundations of Earth Physics(in Chinese).Beijing:Science Press,1985． 276-334
[10] Jaeger J C.Elasticity,Fracture and Flow,212 pp.,Methuen & Co.,London,1964,54-58
[11] Shearer P M.Introduction to Seismology.Cambridge Press, 1999． 15
[12] 王敏中.王炜,武际可.弹性力学教程.北京:北京大学出版社,2002． 80-84 Wang M Z,Wang W,Wu J K.The Course of Elastic Mechanics(in Chinese).Beijing:Beijing University Press,2002． 80-84
[13] A阿拉比,M阿拉比.简明牛津地球科学辞典.陈有发,汤泉,张杰等译.北京:地震出版社,1998． 461 Allaby A,Allaby M.The Concise Oxford Dictionary of Earth Science.Translated by Chen YouFa,Tang Quan,Zhang Jie,et al.Beijing:Seismological Press,1998． 461
[14] Horst Stocker编.物理手册.吴锡英,李祝霞,陈师平译.北京:北京大学出版社,142 Horst Stocker.Physical Handbook.Translated by Wu Xiying,Li Zhuxia,Chen Shi-ping.Beijing:Beijing University Press,142
[15] 万迪堃,汪成民.地下水动态异常与地震短临预报.北京:地震出版社,1993． 10-146 Wan D K,Wang C M.Ground Water Dynamic Anomaly and Short-Term Earthquake Prediction ( in Chinese).Beijing:Seismological Press,1993． 10-146
[16] 敬少群,王佳卫.长沙井动水位对台湾集集7． 6级地震的震时效应及其机理分析.华南地震,2001,21(1) :32-37 Jing S Q,Wang J W.Analysis on seismic effect and its mechanism of Changsha well's dynamic ground water level for the M_s7． 6 Jiji earthquake,Taiwan.South China Journal of Seismology (in Chinese),2001,21(1) :32-37
[17] 张素欣,杨卫东,张子广.唐山矿井模拟与数字水位的记震能力对比分析.西北地震学报,2007,29(2) :170-173 Zhang S X,Yang W D,Zhang Z G.Comparison of the ability of recording seismic wave between digital and analogue groundwater level observation in Tangshan mine well.Northwestern Seismological Journal (in Chinese),2007,29 (2) :170-173
[18] 郑小菁,陈莹.福建数字地下流体网对远处大震映震能力分析.国际地震动态,2007,3:31-37 Zheng X J,Chen Y.Analysis on the reflecting capacity for large distant earthquakes by use of digital underground water monitoring network in Fujian Province.Recent Developments in World Seismology (in Chinese),2007,3:31-37
[19] 晏锐,陈颙,高福旺等.从昌平井体应变、水位对地震波的响应特征求算含水层的SKEMPTON常数.地震学报,2008,30(2) :144-152 Yan R,Chen Y,Gao F W,et al.Calculating B value of aquifer from volume strain and water level response to seismic waves at Changping seismic station.Acta Seismologica Sinica (in Chinese),2008,30(2) :144-152
[20] 《地球科学大辞典》编委会编.地球科学大辞典(基础科学卷).北京:地质出版社,2006． 1-4 The Editorial Committee eds.《Geoscience Big Dictionary》(Basic science volume) (in Chinese).Beijing:Geological Publishing House,2006． 1-4
[21] 汪成民,车用太,万迪堃等.地下水微动态研究.北京:地震出版社,1988． 20-23 Wang C M,Che Y T,Wan D K,et al.Ground Water Micro Dynamics Research (in Chinese).Beijing:Seismological Press,1988,20-23
[22] 国家地震局科技监测司.地震地下流体观测技术.北京:地震出版社,1995． 19 Science,Technology and Monitoring Department of China Earthquake Administration.Seism-Related Underground Fluid Observation Technology ( in Chinese ).Beijing:Seismological Press,1995． 19
[23] 曾劲主编.控制工程基础.北京:电子工业出版社,2007． 18 Edited by Zeng Jing.Control Engineering Foundation (in Chinese).Beijing:Publishing House of Electronics Industry,2007． 18
[24] 陆一心主编.现代工程控制理论.北京:化学工业出版社,2006． 12-21 Edited by Lu YiXin.Modern Engineering Control Theory(in Chinese).Beijing:Chemical Industry Publishing House, 2006． 12-21
[25] 北京大学地球物理系,武汉测绘学院大地测量系,中国科学技术大学地球物理教研室编.重力与固体潮.北京:地震出版社,1982． 349-360 The Earth Physics Department of Peking University,the Geodetic Survey Department of Wuhan Survey Institute,the Geophysics Staff Room of University of Science and Technology of China.Gravity and Earth Tide (in Chinese).Beijing:Seismological Press,1982． 349-360
[26] 张昭栋等.地下水潮汐分析.济南:山东大学出版社,1988． 15-18 Zhang Z D et al.Ground Water Tide Analysis (in Chinese).Jinan:Shandong University Press,1988． 15-18
[27] Brodsky E E,Roeloffs E,Woodcook D,et al.A mechanism for sustained groundwater pressure changes induced by distant earthquakes.Journal of Geophysical Research,2003,108(B8) ,2390,doi:1029/ 2002JB002321,2003,SDE10． 1-10． 4
[28] 邱永平.宁波地震台水位、地倾斜在印尼8． 7、 8． 5级地震中的同震变化现象.内陆地震,2006,20(4) :336-341 Qiu Y P.The phenomenon of co-seism change about water level and the tile of Ningbo seismic station in Indonesia earthquakes with M_s 8． 7 and M_s8． 5． Inland Earthquake (in Chinese),2006,20(4) :336-341
[29] Chia Y P,Wang Y S,Chiu J J,et al.Changes of ground water level due to the 1999 Chi-Chi earthquake in the Choshui River Alluvial Fan.Bulletin of Seismological Society of America,2001,91(5) :1062-1068
[30] Thorne L,Terry C W.Modern Global Seismology.Academic Press,1981． 34-125
[31] 郑小菁,刘序俨,韦永祥,陈莹.采用主成分分析方法研究降水对地下水位的影响.地震,2008,28(4) :91-102 Zheng X J,Liu X Y,Wei Y X,Chen Y.Analysis of effect of precipitation to underground water level of Qingyang stressed well of Fujian Province.Earthquake (in Chinese),2008,28 (4) :91-102
[32] Simon B.Oxford Dictionary of Philosophy.Shanghai:Shanghai Foreign Language Education Press,2000． 267-268
[33] 尹宝军,马丽,陈会忠等.汶川8． 0级地震及其强余震引起的唐山井水位同震响应特征分析.地震学报,2009,31(2) :195-205 Yin B J,Ma L,Chen H Z,et al.Characteristics of coseismic water level change in Tangshan well induced by M_s8． 0 Wenchuan earthquake and its large aftershocks.Acta Seismologica Sinica (in Chinese),2009,31(2) :195-205
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